Advanced Math/bio problems

Course Number: 211G A20

Course Name: Online – Natural History of Life

Instructor: Catherine Hartkorn

Individual/Partner Project - Biology Math Problems Assignment

Remember to write out your calculations and explanations for ALL problems.

Problem Set 4 - Problems on Photosynthesis (3 problems):

9. The fixing of carbon in photosynthesis varies in regard to the amount of ATP needed for each

carbon fixed.

C3 plants use 3 ATPs per carbon

C4 plants use 5 ATPs per carbon

CAM plants use 5.5 ATPs per carbon

If ATP yields 7.3 kilocalories per mole, how many ATP calories are needed to create 1 mole

of glucose (686 kcal/mol) by:

a. a C3 plant? (hint: first, think about how many carbons are in 1 mole of glucose)

b. a C4 plant?

c. a CAM plant?

d. Which type plant uses the most ATP energy in the making of glucose?

10. When light is shined on a leaf, it causes hydrogen ions to be pumped into discs called

thylakoid lumens. The ions then diffuse out through a protein, and in the process an ATP

molecule is made for every three hydrogen ions. While illuminated, inside the disc, the pH can

be as low as 4. Outside the disc, the pH is about 7.2.

A thylakoid lumen can be modeled as a short cylindrical rod that is 80 Å long and 5000 Å in

diameter.

a. How many hydrogen ions are found in one thylakoid lumen of this size at pH 4?

b. How many are found at pH 7.2?

c. How many more ATP molecules can be made from the disc described above,

AFTER the light is turned off?

11. Light is important in biology for photosynthesis. There are two different ways that light is

described in physics.

In the first description, light travels in waves at a fixed speed c = 2.998 x 10 8 meters per second.

The wavelength is the distance from peak to peak of a light wave, and corresponds to the color of

the light. The wavelength is given by λ (the Greek letter lambda). The wavelength varies from

400 nm to 700 nm for light in the visible range, with blue light having λ=450 nm and red light

having λ=680 nm.

The frequency is given by ν (the Greek letter nu). The frequency is the number of peaks that

pass a point in a given time. Frequency is related to wavelength by the formula: ν = c / λ

In the second description, light travels in particles called photons or quanta. Using this

description it makes sense to speak of a mole of light as 6.02 x 10 23

photons.

The energy of one photon of light is given by

E = (hc) / λ = hν

where h is a conversion factor called Planck’s constant; h = 1.583 x 10 -34

calorie seconds.

In the laboratory, light with a very narrow wavelength range can be used for experiments. One

mole of an actinic light (activating light) that has a wavelength of 680 nm was used to excite

chlorophyll, and caused fluorescence measured at a wavelength of 690 nm. The chlorophyll was

isolated, and therefore could do no photochemistry.

a. What is the amount of energy (in kilocalories) in one mole of actinic red light?

b. What is the amount of energy (in kcal) in the light that was fluoresced (assuming

maximal fluorescence)?

c. What is the amount of energy (in kcal) that was lost as heat?

d. What percentage of the red light energy was lost as heat?

A photon of blue light will energize an electron from chlorophyll to a level comparable to a

photon of red light. Suppose blue light energy also caused fluorescence measured at a

wavelength of 690 nm.

e. What percentage of the blue light energy was lost as heat (again assuming maximal

fluorescence)?